KERNEL DENSITY AND HAZARD RATE ESTIMATION FOR CENSORED DATA UNDER α-MIXING CONDITION

ECKHARD LIEBSCHER

Institute of Mathematics, Technical University Ilmenau, 98684 Ilmenau/Thür, Germany, e-mail: lieb@mathematik.tu-ilmenau.de

(Received December 7, 1999; revised July 24, 2000)

Abstract. We derive rates of uniform strong convergence for kernel density estimators and hazard rate estimators in the presence of right censoring. It is assumed that the failure times (survival times) form a stationary α-mixing sequence. Moreover, we show that, by an appropriate choice of the bandwidth, both estimators attain the optimal strong convergence rate known from independent complete samples. The results represent an improvement over that of Cai’s paper (cf. Cai (1998b, J. Multivariate Anal., 67, 23–34)).

Key words and phrases: Kernel density estimator, right censorship, strong convergence, hazard rate estimator.